Is the following biased? Yes, of course it is, I would enjoy watching the team more if he wasn't on it, and what else should I be worried about besides my enjoyment.
I don't know where you picked your starting point but I used August 1 as a best guess, and got 253 PAs. In that stretch, he has a .333 wOBA and a .307 xwOBA. The average RF in baseball this year has a .334 wOBA. So, generously, he's a league average bat for the position. Defensively he's grading out a little above average in the outfield (slash overall). For his career he's got a 97 wRC and is outperforming his xwOBA by 5 points.
Do I think he's an overpay for 2-4 months of Freddy Peralta? Sure, probably, throw in Brooks Raley or Luke Weaver or whatever. I'd probably still lean towards overpackaging the glut of blocked prospects we have.
The point about Shaw having no position but still being on pace for 500 PAs is valid, and I've become convinced there's plenty of PAs available for that 10th man if he can be versatile. Shaw is plenty valuable at that role. I don't think he's nearly as valuable as Starting Corner Outfielder.